Amazon is looking to simplify the name of their video service and brand it with a stronger correlation to their core Prime business.
What makes this perhaps a bit confusing is that this is also the name as advertised to non Prime members. So, if you don’t pay the annual fee for Prime, but browse their video catalog, you will see the Prime logo you are not accustomed to seeing. That does not mean you are magically a free Prime member. You would still have to sign up to get Prime Video perks.
As of press time, Amazon has updated all of their web pages. However, not all of their apps showcase the change. For instance, the Amazon Roku Channel is still named Amazon Video Roku Channel. Whereas in Google Play and the Android app, Prime Video is called Amazon Prime Video.